Adaptive fuzzy neural network finite-time command filtered control of n-link robotic systems with actuator saturation

The finite time tracking control of n-link robotic system is studied for model uncertainties and actuator saturation. Firstly, a smooth function and adaptive fuzzy neural network online learning algorithm are designed to address the actuator saturation and dynamic model uncertainties. Secondly, a new finite-time command filtered technique is proposed to filter the virtual control signal. The improved error compensation signal can reduce the impact of filtering errors, and the tracking errors of system quickly converge to a smaller compact set within finite time. Finally, adaptive fuzzy neural network finite-time command filtered control achieves finite-time stability through Lyapunov stability criterion. Simulation results verify the effectiveness of the proposed control.     

基于有限时间指令滤波的非线性系统固定时间预设性能控制

针对一类严格反馈非线性系统,提出一种基于有限时间指令滤波的自适应固定时间预设性能控制策略.首先,引用非线性映射技术及适当的误差变换,建立等效的误差模型;其次,综合利用反步法、固定时间控制和自适应控制等方法,设计一种基于有限时间指令滤波的预设性能跟踪控制器.该策略应用指令滤波器解决了反步法中对虚拟控制律反复求导问题,减轻了计算负担.此外,预设性能控制和固定时间控制保证了系统的跟踪误差能够在固定时间内收敛到预设性能函数限定的范围内,其收敛时间与系统初始条件无关,且确保系统中全部信号在有限时间均达到有界区域.理论分析与仿真验证均表明了所提出设计方法的有效性.     

Finite-time command filter-based adaptive tracking control for nonstrict feedback nonlinear systems with full-state restrictions and unmodeled dynamics

The finite-time command filter tracking control for a class of nonstrictly feedback nonlinear systems with unmodeled dynamics and full-state constraints is investigated in this paper. The hyperbolic tangent function is used as a nonlinear mapping technique to solve the obstacle of the full-state constraints. A new adaptive finite time control method is proposed through command filtering reverse engineering, and the shortcomings of the dynamic surface control (DSC) method are overcome by the error compensation mechanism. Dynamic signal is designed to handle dynamical uncertain terms. Normalization signal is designed to handle input unmodeled dynamics. Unknown nonlinear functions are approximated by radial basis function neural networks. Based on the Lyapunov stability theory, it is proved that all signals in the closed-loop system are semi-globally consistent and finally bounded and the output tracking error converges in finite time. Two numerical examples are utilized to verify the effectiveness of the proposed control approach.     

Finite-time adaptive neural control for uncertain nonlinear time-delay systems with actuator delay and full-state constraints

This paper investigates finite-time adaptive neural tracking control for a class of nonlinear time-delay systems subject to the actuator delay and full-state constraints. The difficulty is to consider full-state time delays and full-state constraints in finite-time control design. First, finite-time control method is used to achieve fast transient performances, and new Lyapunov–Krasovskii functionals are appropriately constructed to compensate time delays, in which a predictor-like term is utilized to transform input delayed systems into delay-free systems. Second, neural networks are utilized to deal with the unknown functions, the Gaussian error function is used to express the continuously differentiable asymmetric saturation nonlinearity, and barrier Lyapunov functions are employed to guarantee that full-state signals are restricted within certain fixed bounds. At last, based on finite-time stability theory and Lyapunov stability theory, the finite-time tracking control question involved in full-state constraints is solved, and the designed control scheme reduces learning parameters. It is shown that the presented neural controller ensures that all closed-loop signals are bounded and the tracking error converges to a small neighbourhood of the origin in a finite time. The simulation studies are provided to further illustrate the effectiveness of the proposed approach.     

Neuroadaptive containment control of nonlinear multiagent systems with input saturations

This paper investigates the output containment tracking problem of nonlinear multiagent systems with mismatched uncertain dynamics and input saturations. A neural network–based distributed adaptive command filtered backstepping (CFB) scheme is given, which can guarantee that the containment tracking errors reach to the desired neighborhood of origin and all signals in the closed‐loop system are bounded. Note that error compensation system and virtual control laws established in CFB only use local information, so the given scheme is completely distributed. Moreover, the applied sliding mode differentiator (SMD) can make the outputs of SMD fast approximate the virtual signal and its derivative at each step of backstepping, which can further improve the control quality. Finally, a simulation example is given to show the effectiveness of the proposed scheme.     

基于预设性能的非仿射非线性系统自适应有限时间控制

针对一类具有死区的非仿射非线性系统,将预设性能控制与有限时间控制相结合,提出一种具有预设性能的自适应有限时间跟踪控制方法.基于Backstepping技术、模糊逻辑系统及有限时间Lyapunov稳定理论,给出使系统半全局实际有限时间稳定(semi-globally practically finite-time stable,SGPFS)的充分条件和设计步骤.该控制策略不仅使系统的输出误差在有限时间内收敛到一个预先设定区域,同时保证其收敛速度、最大超调量和稳态误差均满足预先设定的性能要求.最后通过仿真示例验证了所提出设计方法的有效性.     

一类机械臂系统自适应有限时间有界H∞跟踪控制

考虑一种电机驱动的单连杆机械臂系统在受到输出约束时的自适应有限时间H∞跟踪控制问题.一个有限时间有界H∞性能的新概念被提出,并结合障碍Lyapunov函数(BLF)、神经网络自适应技术、有限时间控制理论和H∞控制理论,提出了一种该系统在输出受限条件下的自适应神经有限时间有界H∞跟踪控制器设计方法,避免了许多有限时间控制...     

Distributed prescribed performance control for consensus output tracking of nonlinear semi-strict feedback systems using finite-time disturbance observers

The distributed consensus output tracking problem is dealt with for a class of nonlinear semi-strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances and uncertain nonlinear virtual control coefficients of the subsystems. The systems are under a directed communication graph, where the leader node is the root. The controller is designed in a backstepping manner, and the dynamic surface technique is adopted to avoid direct differentiation. At each step of virtual controller design, a prescribed performance controller is constructed to achieve prescribed transient performance so that the system states remain in the feasible domain. Then each virtual controller is enhanced by a finite-time disturbance observer which estimates the disturbance term in a finite-time. The properties of the control system are analysed theoretically. It is clarified that the prescribed performance control technique ensures that the system signals stay in the feasible domain, whereas sufficiently small ultimate control errors can be achieved by the finite-time disturbance observers. Finally, the performance of the proposed methods is confirmed by numerical studies.     

不确定机械臂系统的自适应命令滤波反步渐近跟踪控制

研究具有未知参数和外部干扰机械臂的自适应渐近跟踪控制问题,提出一种自适应命令滤波反步策略,利用命令滤波器避免传统反步中对虚拟控制函数的微分计算,并建立误差补偿机制补偿滤波误差.与现有的针对机械臂的命令滤波反步跟踪控制相比,跟踪误差可以渐近收敛到零,并且只需要设计一个自适应参数.最后,通过仿真验证该方案的有效性.     

Finite-time optimal tracking control for a class of nonlinear systems with prescribed performance

In this paper, a finite-time optimal tracking control scheme based on integral reinforcement learning is developed for partially unknown nonlinear systems. In order to realize the prescribed performance, the original system is transformed into an equivalent unconstrained system so as to a composite system is constructed. Subsequently, a modified nonlinear quadratic performance function containing the auxiliary tracking error is designed. Furthermore, the technique of experience replay is used to update the critic neural network, which eliminates the persistent of excitation condition in traditional optimal methods. By combining the prescribed performance control with the finite-time optimization control technique, the tracking error is driven to a desired performance in finite time. Consequently, it has been shown that all signals in the partially unknown nonlinear system are semiglobally practical finite-time stable by stability analysis. Finally, the provided comparative simulation results verify the effectiveness of the developed control scheme.     

Distributed fuzzy adaptive event-triggered finite-time consensus tracking control for uncertain nonlinear multi-agent systems with asymmetric output constraint

This article investigates the consensus problem for uncertain nonlinear multi-agent systems (MASs) with asymmetric output constraint. Different from BLF-based constraint consensus tracking control, a novel approach based on nonlinear state-dependent function is proposed to solve the asymmetric output constraint, which need not convert output constraint into tracking error bound. First-order sliding mode differentiator is incorporated into each step of backstepping control design to reduce computation burden. Further, in combination of proposed event-triggered mechanism based on time-varying threshold, a distributed fuzzy adaptive event-triggered finite-time consensus method is developed. It can ensure that the consensus tracking error tends to a small neighbor in a finite time and the asymmetric output constraint of each subsystem is not violated. Two simulations are given to demonstrate the effectiveness of control method.     

Command filter-based finite-time adaptive tracking control for MIMO dynamic systems with external disturbances and prescribed performance constraints

This paper investigates command filter-based finite-time stability of multi-input multi-output (MIMO) dynamic systems with prescribed performance constraints and external disturbances. A novel finite-time differentiator is introduced into command filter-based control scheme, which improves transient performance of each subsystem. Meanwhile, disturbance observers are utilized to eliminate negative effects on control system caused by external disturbances. Furthermore, featured with a selected performance function, it can be guaranteed that tracking errors remain in prescribed performance region. Stability analysis of the proposed controller is presented by using a Lyapunov function including transformed filter errors, parameter errors of neural networks, and observed errors of lumped disturbances. Effectiveness of proposed control method is verified by a numerical example and a practical system of inverted pendulums, respectively.     

一类非线性大系统分散自适应预设性能有限时间跟踪控制

研究一类非线性互联大系统的分散自适应预设性能有限时间跟踪控制问题.结合神经网络自适应技术、实际有限时间控制理论和预设性能控制方法,提出一种新的预设性能控制设计方法,以解决传统预设性能方法难以实现分散控制的问题.所设计的控制器能够保证大系统中各个子系统的跟踪误差被有限时间性能函数约束,在任意给定的停息时间内收敛到平衡点的一个给定的邻域内,且该闭环大系统的所有信号是实际有限时间稳定的.特别地,该停息时间与系统初始状态无关.两个仿真例子验证了所提出控制方法的有效性和优越性.     

具有全状态约束和未建模动态的严格反馈系统有限时间自适应动态面控制

针对一类具有全状态约束、未建模动态和动态扰动的严格反馈非线性系统,通过构造非线性滤波器,并利用Young’s不等式,提出一种新的有限时间自适应动态面控制方法.引入非线性映射处理全状态约束,将有约束系统变成无约束系统,利用径向基函数逼近未知光滑函数,利用辅助系统产生的动态信号处理未建模动态.对于变换后的系统,利用改进的动态面控制和有限时间方法设计的控制器结构简单,移去现有有限时间控制中出现的“奇异性”问题,可加快系统的收敛速度.理论分析表明,闭环系统中的所有信号在有限时间内有界,全状态不违背约束条件.数值算例的仿真结果表明,所提出的自适应动态面控制方案是有效的.     

Neural network-based robust finite-time control for robotic manipulators considering actuator dynamics

A novel neural network-based robust finite-time control strategy is proposed for the trajectory tracking of robotic manipulators with structured and unstructured uncertainties, in which the actuator dynamics is fully considered. The controller, which possesses finite-time convergence and strong robustness, consists of two parts, namely a neural network for approximating the nonlinear uncertainty function and a modified variable structure term for eliminating the approximate error and guaranteeing the finite-time convergence. According to the analysis based on the Lyapunov theory and the relative finite-time stability theory, the neural network is asymptotically convergent and the controlled robotic system is finite time stable. The proposed controller is then verified on a two-link robotic manipulator by simulations and experiments, with satisfactory control performance being obtained even in the presence of various uncertainties and external disturbances.     

Filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties

This paper synthesizes a filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties. The multivariable nonlinear systems under consideration have both matched and mismatched uncertainties, which satisfy the semiglobal Lipschitz condition. The nonlinear uncertainties are approximated by a Gaussian radial basis function (GRBF)‐based neural network incorporated with a piecewise constant adaptive law, where the adaptive law will generate adaptive parameters by solving the error dynamics between the real system and the state predictor with the neglection of unknowns. The combination of GRBF‐based neural network and piecewise constant adaptive law relaxes hardware limitations (CPU). A filtering control law is designed to handle the nonlinear uncertainties and deliver a good tracking performance with guaranteed robustness. The matched uncertainties are cancelled directly by adopting their opposite in the control signal, whereas a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. Since the virtual reference system defines the best performance that can be achieved by the closed‐loop system, the uniform performance bounds are derived for the states and control signals via comparison. To validate the theoretical findings, comparisons between the model reference adaptive control method and the proposed filtering adaptive neural network control architecture with the implementation of different sampling time are carried out.     

基于控制性能的MIMO非线性系统动态面控制

针对一类不确定非线性MIMO(multiple-input multiple-output)系统,在动态面控制方法的基础上,提出了自适应跟踪控制方案.通过引入性能函数和输出误差转换,保证输出信号具有指定的跟踪速度、跟踪误差、最大超调量.为了避免控制奇异问题,采用神经网络直接逼近期望控制信号.该方案无需估计神经网络的权值,仅对1个参数进行自适应律设计.理论证明了闭环系统所有信号有界,仿真结果验证了所提方案的有效性.     

Predefined-time control for Euler–Lagrange systems with model uncertainties and actuator faults

A novel adaptive predefined-time tracking control algorithm is proposed for the Euler–Lagrange systems (ELSs) with model uncertainties and actuator faults. Compared with traditional finite-time and fixed-time studies, the system output tracking error under the proposed predefined-time controller converges to a small neighborhood of zero in finite time, whose upper bound is exactly a design parameter in the control algorithm. For the uncertain model, radial-based function neural network (RBFNN) is utilized to approximate the continuous uncertain dynamics. To deal with the actuator faults, an adaptive control law is involved in the fault-tolerant controller. In order to achieve the predefined-time bounded, a novel predefined-time sliding mode surface is designed. It is proved that the tracking error vector trajectory of closed-loop system is semi-globally uniformly ultimately predefined-time bounded, and the upper bounds of both the system settling time and the corresponding output tracking error can be adjusted with a simple parameter. Simulation examples finally demonstrate the effectiveness of the proposed control algorithm.     

Adaptive Fuzzy Finite-time Dynamic Surface Control for High-order Nonlinear System with Output Constraints

This paper studies the problem of finite-time fuzzy adaptive dynamic surface control (DSC) design for a class of single-input and single-output (SISO) high-order nonlinear systems with output constraint. Fuzzy logic systems (FLSs) are utilized to identify the unknown smooth functions. By adopting Barrier Lyapunov function (BLF), the problem of output constrain is handled. Combining adding a power integrator and adaptive backstepping recursion design technique, a novel fuzzy adaptive finite-time DSC algorithm is proposed. Based on finite-time Lyapunov stable theory, the developed control algorithm means that all the signals of the closed-loop system are semi-global practical finite-time stable (SGPFS) and the tracking error converges to a small neighborhood of origin in finite time. In addition, the output does not violate the given constrain bound. Finally, both numerical and practical simulation examples are given to illustrate the effectiveness of the proposed control algorithm.

     

Disturbance-observer-based adaptive finite-time dynamic surface control for PMSM with time-varying asymmetric output constraint

This article presents a disturbance-observer-based adaptive finite-time dynamic surface control scheme, capable of guaranteeing transient behavior for the PMSM with arbitrary asymmetric time-varying output constraint and unmatched external disturbance. The major challenge of this paper is devising efficient strategies to tackle the nonsymmetric output restraints with arbitrary characteristics and unmatched external perturbation for the system under the finite-time backstepping framework. Given this, a nonlinear transformation function is adopted to coordinate from the output-constrained dynamic model to an uncontained one, and a finite-time disturbance observer is introduced to evaluate the unmatched external perturbation. Then, a dynamic surface control approach having adaptive properties for PMSM is conceived by combing a neural network to evaluate the nonlinear functions and a first-order filter to handle the “explosion of complexity.” Additionally, it is proved that the signals in the closed-loop system can narrow down to a bounded region and the tracking error can merge in a limited time to tiny vicinity of zero by employing a fast finite-time stability principle. Eventually, simulation cases and contrast results reveal the tracking performance and immunity to the disturbance of the devised controller.